How do i find the exact value of the trigonometric function (sin(3pi/2)) without just puttingit in my calculator?

Question

We are studying trig functions and general angles in class and I don't understand how to calculate the function with out using my calculator to get the answer AND showing my work.

 

***Sorry I don't have a "pi" button on my computer

Answer 1

Ally, whenever the problem says, "find the exact value", you can't use your calculator.

 

Calculators only give approximate answers, no matter how many decimals it gives.

 

pi, as a symbol, is considered an exact value; whereas 3.141592653589793 from the calculator is considered an approximate value.

 

Every point on the Unit Circle (radius 1) has coordinates (cos(θ),sin(θ)). 3pi/2 = 270°, so its point on the Unit Circle is

(0,-1) = (cos(3pi/2),sin(3pi/2)).

So –1 = sin(3pi/2).

Answer 2

Sin ( 3∏/2) = -1

 

  3∏/2 is  270 °, and is located on the end of the 3rd quarter, and beginning of 4th quarter on unit circle.

 

Sin ( 3∏/ 2) = - Sin∏/2 = -1